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In this paper, the prediction of the lifetime of k-component coherent systems is studied using classical and Bayesian approaches with type-II censored system lifetime data. The system structure and signature are assumed to be known, and the component lifetime distribution follows a half-logistic model. Various point predictors, including the maximum likelihood predictor, the best-unbiased predictor, the conditional median predictor, and the Bayesian point predictor under a squared error loss function, are calculated for the coherent system lifetime. Since the integrals required for Bayes prediction do not have closed forms, the Metropolis-Hastings algorithm and importance sampling methods are applied to approximate these integrals. For type-II censored lifetime data, prediction interval based on the pivotal quantity, prediction interval HCD, and Bayesian prediction interval are considered. A Monte Carlo simulation study and a numerical example are conducted to evaluate and compare the performances of the different prediction methods.

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In many applications, observations have a skewness, an elongated shape, a heavy tail, a multi-mode structure, or a mixed distribution. Therefore, models based on the normal distribution cannot provide correct inferences under such conditions and can lead to biased estimators or increased variance. The Laplace distribution and its generalizations can be suitable alternatives in such situations due to their elongation, heavy tails, and skewness. On the other hand, in models based on mixed distributions, there is always a possibility that fewer samples are available from one or more components. Therefore, given the Bayesian approach's advantage in handling small samples, this research developed a Bayesian model to fit a finite mixed regression model with skew-Laplace distributions and conducted a simulation study to assess its performance. Laplace has been compared in two approaches, frequentist and Bayesian. The results show that the Bayesian approach of the model is more effective than other  models.